Title: 3D Mandelbrot (a newbies attempt) Post by: gengis on September 08, 2010, 11:26:53 PM I have seen a few things in this forum looking something like what I have in mind, but only quite. What I have in mind is 3D-Mandelbrot which, when sliced at z=0 actually looks like the 2D-Mandelbrot.
here my attempt: expand the rules for multiplication and summation of complex numbers to the 3rd dimension: Z(n) = Z(n-1)^2 + C would then mean convert Z(n-1) from Cartesian to spherical coordinates multiply the lengths and add the angles, convert it back to Cartesian and add C I have done 256 iterations but only on a 154x154x154 array. here the results. an isosurface on points which are finite: count how many iterations it takes for vector length to exceed 4. plot a isosurface for each iteration 256 to 1 in steps of 4. each isosurface with a alpha of 0.1: tell me what you think... Title: Re: 3D Mandelbrot (a newbies attempt) Post by: Tglad on September 09, 2010, 12:03:03 AM yes that's a mandelbulb. There are 3 mandelbulbs despite most images being of just one of them (an arbitrary choice because it looks a bit more bulby).
In fact there are as many mandelbulbs as there are orientations, the 3 are 90 degrees apart from each other in that sense... there is a video from about last dec showing the mandelbulbs in this space... the full set may have been called the hopfbulb or hopfbrot I forget. Title: Re: 3D Mandelbrot (a newbies attempt) Post by: M Benesi on September 09, 2010, 03:15:43 AM Yeah, an oldie but a goodie.
It's the equivalent of taking: the complex number z1= sqrt(start_x^2 +start_y^2) + i start_z real_z1= real part of z1 imag_z1= imaginary part of z1 the complex number z2= start_x + i start_y real_z2= real part of z2 imag_z2= imaginary part of z2 magnitude of z2, r = sqrt (start_x^2 +start_y^2) z1= z1 ^ n z2= z2 ^ n r= r ^ -n new_x = real_z1 * real_z2 *r new_y = real_z1 * imag_z2 *r new_z = imag_z1 add in your pixel values appropriately, so on and so forth.... However, the really detailed one is the "opposite" complex triplex: you take: z1 = start_x + i sqrt(start_y^2+ start_z^2)... etc... You don't get a 2d mandelbrot shape, but then again you shouldn't expect one due to the mathematics involved (as the 2d brot is skewed over the y axis, you get a double skew due to the 2 imaginary components for the 3d version, rather than a simple single skew).... Title: Re: 3D Mandelbrot (a newbies attempt) Post by: Nahee_Enterprises on September 12, 2010, 11:16:54 PM I have seen a few things in this forum looking something like what I have in mind, but only quite. What I have in mind is 3D-Mandelbrot which, when sliced at z=0 actually looks like the 2D-Mandelbrot. ........... tell me what you think... Greetings, and Welcome to this particular Forum !!! :) I think that people are still trying to define and discover the TRUE 3D-Mandelbrot. Title: Re: yet another "true" 3d-fractal Post by: EvaB on January 03, 2011, 11:10:27 AM I think that people are still trying to define and discover the TRUE 3D-Mandelbrot. So do I - another newbie's attempt: (http://members.aon.at/evab/titelbild.png) z=a+bi+cj z2=(a2-2bc) + i (2ab-c2) + j (2ac-b2) with a special multiplication: ii=-j jj=-i ij=ji=-1 e=1 ei=ie=i ej=je=j http://members.aon.at/evab/ (http://members.aon.at/evab/) (german, but less text, more images) |